As the semiconductor technology continues to develop, hundreds of cores will be deployed on a single die in the future Chip-Multiprocessors (CMPs) design. Three-Dimensional Network-on-Chips (3D NoCs) has become an attractive solution which can provide impressive high performance. An efficient and deadlock-free routing algorithm is a critical to achieve the high performance of network-on-chip. Traditional methods based on deterministic and turn model are deadlock-free, but they are unable to distribute the traffic loads over the network. In this paper, we propose an efficient, adaptive and deadlock-free algorithm (EAR) based on a novel routing selection strategy in 3D NoC, which can distribute the traffic loads not only in intra-layers but also in inter-layers according to congestion information and path diversity. Simulation results show that the proposed method achieves the significant performance improvement compared with others.